integral from ln(4) to ln(25) of e^{x/2}

Lösung

\int_{l n (4)}^{l n (25)} e^{\frac{x}{2}} d x

6

Schritte zur Lösung

\int_{l n (4)}^{l n (25)} e^{\frac{x}{2}} d x

Wende U-Substitution an

= \int_{l n (2)}^{l n (5)} e^{u} \cdot 2 d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{l n (2)}^{l n (5)} e^{u} d u

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= 2 [e^{u}]_{l n (2)}^{l n (5)}

Berechne die Grenzen:

3

= 2 \cdot 3

Vereinfache

= 6

x \to 0 lim (- \frac{5}{1 - 5 x})

\frac{d y}{d x} = \frac{1}{1 - x}, y (0) = 1

d er i v a t i v e f (x) = \frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}}

t an g e n t x^{3} - x^{2} + 1

\int x \cdot ln (\frac{1 - x}{1 + x}) d x